Method for interactive viewing full-surround image data and apparatus therefor

ABSTRACT

A method of modeling of the visible world using full-surround image data includes steps for selecting a view point within a p-surface, and texture mapping full-surround image data onto the p-surface such that the resultant texture map is substantially equivalent to projecting full-surround image data onto the p-surface from the view point to thereby generate a texture mapped p-surface. According to one aspect of the invention, the method also includes a step for either rotating the texture mapped p-surface or changing the direction of view to thereby expose a new portion of the texture mapped p-surface. According to another aspect of the invention, a first the texture mapped p-sphere is replaced by a second texture mapped p-sphere by interactively selecting the new viewpoint from viewpoints within the second texture mapped p-sphere. A corresponding apparatus is also described.

This application is a provision of 60/071,148 filed Jan. 12, 1998 and aContinuation-in-Part of Ser. No. 08/749,166, which was filed on Nov. 14,1996 (now U.S. Pat. No. 5,903,782).

BACKGROUND OF THE INVENTION

The present invention relates generally to a method and correspondingapparatus for viewing images. More specifically, the present inventionrelates to a method and corresponding apparatus for viewingfull-surround, e.g., spherical, image data;

Systems and techniques for changing the perspective of a visible imagein producing a resultant image, or systems and methods of transformingan image from one perspective form to another have been the subject ofscientific thought and research for many years. Systems and techniquesfor transforming visible images can generally be divided into threeseparate categories:

(1) perspective generation systems and methods suitable for applicationssuch as flight simulators;

(2) three-dimensional (3D) to two-dimensional (2D) conversion systemsand methods; and

(3) miscellaneous systems and methods.

The first category includes U.S. Pat. No. 3,725,563, which discloses amethod of and apparatus for raster scan transformations usingrectangular coordinates which are suitable for electronically generatingimages for flight simulators and the like. More specifically, the patentdiscloses a technique for raster shaping, whereby an image containinginformation from one viewpoint is transformed to a simulated image fromanother viewpoint. On the other hand, U.S. Pat. No. 4,763,280 disclosesa curvilinear dynamic image generation system for projecting rectangularcoordinate images onto a spherical display surface. In the disclosedsystem, rectangular coordinates are converted to spherical coordinatesand then the spherical coordinates are distorted for accomplishing thedesired simulation of curvature.

The second category of systems and techniques perform 3D-to-2Dconversion, or vice versa. For example, U.S. Pat. No. 4,821,209discloses a method of and apparatus for data transformation and clippingin a graphic display system, wherein data transformation is accomplishedby matrix multiplication. On the other hand, U.S. Pat. No. 4,667,236discloses a television perspective effects system for providingperspective projection whereby each point of a three-dimensional objectis projected onto a two-dimensional plane. New coordinates X′ and Y′ areprepared from the original coordinates X, Y and Z, and the viewingdistance D, using the general formulas X′=XD/Z and Y′=YD/Z. As theobject to be displayed is rotated around the X or Y axis, the viewingdistance D is changed for each point.

In the third category, miscellaneous systems and methods are disclosedby, for example, U.S. Pat. No. 5,027,287, which describes a device forthe digital processing of images to obtain special geometrical effectswherein digital image data corresponding to intersection points on arectangular X,Y grid are transposed by interpolation with respect tointersection points of a curved surface. U.S. Pat. No. 4,882,679, on theother hand, discloses a system and associated method of reformattingimages for three-dimensional display. The disclosed system isparticularly useful for generating three-dimensional images from datagenerated by diagnostic equipment, such as magnetic resonance imaging.

However, none of the above described methods or systems permit viewingin circular perspective, which is the best way to view spherical data.Circular perspective does all that linear perspective does when zoomedin, but it allows the view to zoom out to the point where the viewer cansee almost everything in the spherical data simultaneously in a visuallypalatable and coherent way.

What is needed is a method for viewing full-surround, e.g., spherical,image data employing circular perspective. Moreover, what is needed isan apparatus for viewing fall-surround, e.g., spherical, image dataemploying circular perspective. What is also needed is a method forviewing full-surround, e.g., spherical, image data employing circularperspective which is computationally simple. Preferably, the method forviewing full-surround, e.g., spherical, image data employing circularperspective can be employed on any personal computer (PC) systempossessing a three dimensional (3-D) graphics capability.

SUMMARY OF THE INVENTION

Based on the above and foregoing, it can be appreciated that therepresently exists a need in the art for viewing methods and correspondingapparatuses which overcome the above-described deficiencies. The presentinvention was motivated by a desire to overcome the drawbacks andshortcomings of the presently available technology, and thereby fulfillthis need in the art.

The present invention implements a novel and practical circularperspective viewer for spherical data. Moreover, it implements thecircular perspective viewer within the context of existing 3D graphicsutilities native to personal computers (PCs). Thus, the method andcorresponding apparatus for circular perspective viewing is practicalfor a broad market.

One object according to the present invention is to provide a method andcorresponding apparatus for modeling the visible world by texturemapping full-surround image data.

Another object according to the present invention is to provide a methodand corresponding apparatus for modeling the visible world by texturemapping full-surround image data onto a p-surface whereby the resultanttexture map is substantially equivalent to projecting full-surroundimage data onto the p-surface from a point Q inside the region X of thep-surface.

Still another object according to the present invention is to provide amethod and corresponding apparatus for modeling the visible world bytexture mapping full-surround image data wherein the viewer is allowedto interactively rotate the model.

Yet another object according to the present invention is to provide amethod and corresponding apparatus for modeling the visible world bytexture mapping full-surround image data wherein the viewer is allowedto interactively change the direction of vision.

A still further object according to the present invention is to providea method and corresponding apparatus for modeling the visible world bytexture mapping full-surround image data, wherein the viewer is allowedto interactively alter the focal length or view angle.

Another object according to the present invention is to provide a methodand corresponding apparatus for modeling the visible world by texturemapping full-surround image data, wherein the viewer is allowed tointeractively move the viewpoint.

Still another object according to the present invention is to provide amethod and corresponding apparatus for modeling the visible world bytexture mapping full-surround image data, wherein the viewpoint is closeto the surface of the p-sphere.

Another object according to the present invention is to provide a methodand corresponding apparatus for modeling the visible world by texturemapping full-surround image data, wherein the viewer is allowed tointeractively direction of view.

A further object according to the present invention is to provide amethod and corresponding apparatus for modeling the visible world bytexture mapping full-surround image data, wherein the viewer is allowedto select an area of the image and cause another model of the visibleworld to be loaded into said viewing system.

Another object according to the present invention is to provide a methodand corresponding apparatus for modeling the visible world by texturemapping full-surround image data, wherein the viewer is allowed toperform any combination of actions specified immediately above.

It will be appreciated that none of the above-identified objects needactually be present in invention defined by the appended claims. Inother words, only certain, and not all, objects of the invention havebeen specifically described above. Numerous other objects advantageouslymay be provided by the invention, as defined in the appended claims,without departing from the spirit and scope of the invention.

These and other objects, features and advantages according to thepresent invention are provided by a method of modeling the visible worldusing full-surround image data. Preferably, the method includes stepsfor selecting a view point within a p-surface, and texture mappingfull-surround image data onto the p-surface such that the resultanttexture map is substantially equivalent to projecting full-surroundimage data onto the p-surface from the view point to thereby generate atexture mapped p-surface.

According to one aspect of the invention, the method also includes astep for either rotating the texture mapped p-surface or changing thedirection of view to thereby expose a new portion of the texture mappedp-surface. According to another aspect of the invention, a first thetexture mapped p-sphere is replaced by a second texture mapped p-sphereby interactively selecting the new viewpoint from viewpoints within thesecond texture mapped p-sphere.

These and other objects, features and advantages according to thepresent invention are provided by a method of modeling of the visibleworld using full-surround image data, the method comprising steps forproviding the full surround image data, selecting a view point within ap-surface, texture mapping full-surround image data onto the p-surfacesuch that the resultant texture map is substantially equivalent toprojecting full-surround image data onto the p-surface from the viewpoint to thereby generate a texture mapped p-surface, and displaying apredetermined portion of the texture mapped p-sphere.

These and other objects, features and advantages according to thepresent invention are provided by an apparatus for modeling the visibleworld using full-surround image data, comprising first circuitry forselecting a view point within a p-surface, second circuitry for texturemapping full-surround image data onto the p-surface such that theresultant texture map is substantially equivalent to projectingfull-surround image data onto the p-surface from the view point tothereby generate a texture mapped p-surface, and third circuitry fordisplaying a predetermined portion of the texture mapped p-sphere.

These and other objects, features and advantages of the invention aredisclosed in or will be apparent from the following description ofpreferred embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

These and various other features and aspects of the present inventionwill be readily understood with reference to the following detaileddescription taken in conjunction with the accompanying drawings, inwhich like or similar numbers are used throughout, and in which:

FIG. 1 illustrates a set of all rays from a predetermined viewpoint,which illustration facilitates an understanding of the presentinvention;

FIG. 2 illustrates a set of points, excluding the viewpoint, located ona corresponding one of the rays, which illustration facilitates anunderstanding of the present invention;

FIG. 3 illustrates the formation of a projection of the set of points,or a subset thereof, illustrated in FIG. 2;

FIGS. 4A and 4B illustrate the resultant images generated by twodifferent projections, respectively, given a constant viewpoint;

FIG. 5 illustrates the concept of linear perspective:

FIG. 6 illustrates the concept of circular perspective;

FIG. 7 illustrates the concept of stereographic projection;

FIG. 8 is a high level block diagram of a circular perspective viewingsystem according to the present invention;

FIGS. 9A through 9G collectively form a listing of the dedicated codefor converting a general purpose computer system into the circularperspective viewing system illustrated in FIG. 8; and

FIGS. 10A and 10B collectively forming a listing of an exemplary codeblock for triangulating a hemisphere and texture coordinates.

DETAILED DESC

RIPTION OF THE PREFERRED EMBODIMENTS The method and correspondingapparatus according to the present invention are similar to thatdisclosed in U.S. Pat. No. 5,684,937, which patent is incorporatedherein by reference for all purposes, in that it generates perspectiveviews derived for constants less than or equal to two, and greater thanor equal to one, i.e., 1.0≦X≦2.0. However, it will be appreciated thatthe inventive method and apparatus are different from U.S. Pat. No.5,684,937 in that the method for deriving perspective is different than‘explicitly’ dividing all angles by a selected constant, as disclosed inthat patent. Instead, the angles are ‘implicitly’ divided by a constantby moving the viewpoint around inside a “p-sphere”. Additional detailswill be provided below.

By employing the method and corresponding apparatus according to thepresent invention, it is possible to create a virtual pictosphere usinga conventional 3-D graphics system. Preferably, the inventive method andapparatus texture map the visible world onto a sphere. It should bementioned that when the user selects a viewpoint at the center of thissphere and renders the view using the primitives of a conventional 3Dgraphics system, the user implicitly divides all angles by one, andresults in a linear perspective view. However, when the user selects aviewpoint on the surface of this sphere, selects a direction of viewtowards the center, and renders the view using the primitives of aconventional 3D graphics system, the user implicitly divides all anglesby two, thus creating a circular perspective view. Moreover, by allowingthe viewpoint to move around within or on the sphere, the user achievesresults virtually identical to those achieved by U.S. Pat. No. 5,684,937for constants ranging from 1.0 to 2.0.

It will be appreciated that the method and corresponding apparatusaccording to the present invention implement a novel and practicalcircular perspective viewer of spherical data. The inventive method andapparatus advantageously can be achieved within the context of existing3-D graphics utilities and hardware native to PCs. It will be noted fromthe statement immediately above that the inventive method and apparatusadvantageously can be implemented in a broad range of existing systems.

The method and corresponding apparatus according to the presentinvention are predicated on the following starting, i.e., given,conditions:

(1) the set of all rays V from a given point VP, as illustrated in FIG.1;

(2) a set of points P not including VP, each point in P being containedby one and only one ray in V, as illustrated in FIG. 2; and

(3) the set of color values C, each color in C being associated with oneand only one ray in V, and also thereby associated with the point in Pcontained by said ray.

Moreover, the following definitions apply:

(1) POINTS P: The visible world.

(2) A PROJECTION OF P: A subset of points P. Any number of points Pncontained in P may be slid closer to or further from point VP alongtheir corresponding rays. The resultant new configuration of points P iscalled a projection of P. The concept can best be understood byreferring to FIG. 3;

(3) MAGIC POINT, VIEWPOINT, OR POINT OF PROJECTION: Point VP. Pleasenote, no matter how points P are projected, their appearance will remainthe same when viewed from point VP. This latter concept may best beunderstood by referring to FIGS. 4A and 4B.

(4) FULL-SURROUND IMAGE DATA: data which samples the points P. This dataencodes, explicitly or implicitly, the association of a color value witha given direction from a given point of projection. It should bementioned at this point that full-surround image data is useful in manyfields of entertainment because, when delivered to many viewers, itenables the construction of an independent viewing system defined below.

(5) P-SPHERE: a computer graphics representation of any polyhedron wherethere exists at least one point x inside (neither intersecting, norlying outside) the polyhedron which may be connected to every point ofthe polyhedron with a distinct line segment, no portion of which saidline segment lies outside the polyhedron or intersects the polyhedron ata point not an endpoint. The union of all such points x form the regionX of the p-sphere. For a convex p-sphere, the region X is all points ofthe interior of the p-sphere. Examples of computer graphics objectswhich may be modeled as p-spheres include a tetrahedron, a cube, adodecahedron, and a faceted sphere.

(6) P-SURFACE: a computer graphics representation of any surface with awell-defined inside and outside, where there exists at least one point xinside (neither intersecting, nor lying outside) the surface which maybe connected to every point of the surface with a distinct line segment,no portion of which said line segment lies outside the surface orintersects the surface at a point not an endpoint. The union of all suchpoints x form the region X of the p-surface. For a convex p-surface, theregion X is all points of the interior of the p-surface. Examples ofcomputer graphics objects which may be modeled as p-surfaces:tetrahedron, cube, sphere, ellipsoid, cylinder, apple torus, lemontorus, b-spline surfaces closed or periodic in u and v. A p-sphere is ap-surface.

(7) LINEAR PERSPECTIVE: the projection of a portion of the visible worldonto a plane or portion of a plane, as illustrated in FIG. 5.

(8) CIRCULAR PERSPECTIVE: the projection of the visible world, orportion thereof onto a plane, or a portion of a plane, after performingthe perspective transformation of the visible world according to U.S.Pat. No. 5,684,937, where the constant used is 2. After such atransformation, when the direction of vision specified in saidtransformation is perpendicular to the projection plane, there is aone-to-one mapping of all the points P defining the visible world andall the points of an infinite plane. This definition is illustrated inFIG. 6;

(9) STEREOGRAPHIC PROJECTION: the one-to-one mapping of each point on asphere to each point of an infinite tangent plane, said mappingperformed by constructing the set of all rays from the antipodal pointof the tangent point, the intersection of said rays with the planedefining said mapping. The understanding of this definition will befacilitated by reference to FIG. 7. Please note that circularperspective and stereographic projection produce geometrically similar(identically proportioned) mappings when the direction of visionspecified in the perspective transformation of circular perspectivecontains the tangent point specified in stereographic projection;

(10) INDEPENDENT VIEWING SYSTEM: an interactive viewing system in whichmultiple viewers can freely, independently of one another, andindependently of the source of the image data, pan that image data inall directions with the effect that each viewer feels like they are“inside” of that imagery, or present at the location from which theimagery was produced, recorded, or transmitted; and

(11) STANDARD COMPUTER GRAPHICS SYSTEM: a computer graphics system whichsupports linear perspective viewing, including the changing of the focallength or the altering of the view angle, the apparent rotation ofviewed objects, and/or the apparent changing of direction of vision, andthe texture mapping of image data onto objects within the class ofp-surface.

It will be appreciated that in a standard computer graphics system bytexture mapping full-surround image data onto a p-surface such that theresultant texture map is effectively equivalent to projecting thefull-surround imagery onto the p-surface from a some point Q containedin the region X of the p-surface, a representation of the visible worldis achieved.

Referring to FIGS. 9A through 9G, the method for viewing full-surround,e.g., spherical, image data will now be described. It should bementioned that the corresponding code implementing the inventive methodis written in the “C” language, although a plurality of programminglanguages are well known and readily adapted to this purpose. It willalso be appreciated that code lines starting with “gl” or “glut”indicate calls to a conventional graphics library (GL) such as OpenGL™.One of ordinary skill in the art will readily appreciate that the lastfunction in this listing is called main. This is where the programstarts.

It will be appreciated from inspection of FIGS. 9A through 9G that theroutine main calls various glut . . . functions to set up GL, thegraphics library used here. It will be noted that the glut... functionsare part of GL. Furthermore, it will be appreciated that main registersor maps certain keyboard events with GL with glutKeyboardFunc(Key). Inother words, glutKeyboardFunc(Key) defines the response of the inventivemethod to operation of the corresponding “Key.”

Moreover, Key is a function describing the actions of GL to keyboardevents. Of importance are keyboard events (‘z’ and ‘Z’) which move theviewpoint in and out along the Z axis relative to the “p-sphere”,effectively altering the perspective of the view, and keyboard events(55, 57, 52, 54, 56 and 50) which control rotation of the “p-sphere”,effectively allowing the viewer to “look around”.

It will be noted that main registers the function display with GL,with the glutDisplayFunc(display) function. Moreover, display uses theglobal variables controlled by Key to move the viewpoint along the Zaxis relative to the “p-sphere”, and to rotate the “p-sphere” relativeto a constant direction of view.

Preferably, display builds the “p-sphere” withglCallList(current_texture->tex1) and glCallList(current_texture->tex2).In the first instance, tex1 is mapped to a triangulation approximating ahemisphere, and is added to the display list. In the second instance,tex2 is mapped to the same hemisphere—after rotating it 180 degrees toform a sphere—and is also added to the display list, in the functionreadTexture. Preferably, tex1 and tex2 are texture maps built from twopictures, respectively, taken with a fisheye lens. Advantageously, tex1and tex2 collectively comprise a “pictosphere.” It should be noted thatthe triangulation approximating the hemisphere was built in the functioncreateHemisphere, the full listing of which is found in FIGS. 10A and10B and not FIGS. 9A-9G.

At this point, Key and display have been registered with GL. The codemain then calls initialize_objects which actually calls the routinesreadTexture and createHemisphere. All the other functions are supportfunctions.

It will be appreciated that the user now has an instance of a p-spherein GL made by mapping two fisheye images, e.g., photographs, to twoadjoining hemispheres to thereby generate full-surround, e.g.,spherical, image data. The user advantageously can interactively movethe viewpoint away from the center of the p-sphere and, if so desired,very near the inside surface of the p-sphere. It should be mentioned atthis point that the direction of view is still towards the center of thep-sphere. Moving the viewpoint from the center of the p-sphereautomatically generates a circular perspective view, whichadvantageously can be displayed on display screen 20 of the PCillustrated in FIG. 8. Moving back to the center of the p-sphere,permits the user to generate a linear perspective view. It will also beappreciated from the discussion above that it is possible to rotate thesurface of p-sphere, thus simulating looking around within the p-sphere.

It should be mentioned that by setting the viewpoint of the graphicssystem close to the center point of the p-sphere point and then enablingthe viewer to rotate that p-sphere around a point close to the centerpoint of the p-sphere, an independent viewing system providing linearperspective is achieved. Moreover, by adding the further capability ofaltering the focal length or angle of view, a zoom abilityadvantageously can be provided for the user.

It should also be mentioned that in the case where the p-surface used tomodel the visible world is a good approximation of a sphere, that is, asubstantially better model than a tetrahedron or a cube, and where theview point of that representation is close to the approximate center ofthat p-surface, then by allowing the viewer to move the viewpoint awayfrom center point to a point close to the surface of the p-surface, anindependent viewing system is achieved in circular perspective. This isastounding when one considers that the native graphics system of aconventional PC only supports viewing in linear perspective. The methodand corresponding apparatus according to the present invention workbecause such an independent viewing system models stereographicprojection, which is geometrically similar to circular perspective.

Furthermore, by letting the viewer move the viewpoint outside of thep-surface, the viewer can get a feeling for how the independent viewingworks. This can be useful for designers of systems containing manyhyper-linked full-surround surfaces. For example, many p-spherespicturing the penthouse terraces of New York advantageously can belinked together so that the viewer may hop from p-sphere to p-sphere,simulating a tour of the terraces.

The above described method of the invention may be performed, forexample, by the apparatus shown in FIG. 8. This viewing apparatus iscomposed of a central processing unit (CPU) 10 for controlling thecomponents of the system in accordance with a control program stored inread-only memory (ROM) 60 or the like. The CPU 10 stores temporary dataused during execution of the inventive method, i.e., viewing method, inrandom-access memory (RAM) 40. After the majority of the method stepsare performed, the generated visible points are displayed on displaydevice 20 (e.g., cathode ray tube (CRT) or liquid crystal display (LCD))as visible points in accordance with the appropriate color values storedin color table 30, e.g., a color lookup table (CLUT) found in thegraphics controller in most PCs. Advantageously, a spherical datagenerator device 70, such as a camera or the like, and preferably thedata generator system disclosed in U.S. Pat. No. 5,903,782, which Patentis incorporated herein by reference for all purposes, may be used togenerate different color values corresponding to the visible points of aviewed object, image or picture. An input device 50 is provided forentering data such as the viewer's viewing direction, reference plane,configuration (scaling) factor k, and other pertinent information usedin the inventive viewing method.

As mentioned above, it will be appreciated that the method andcorresponding apparatus according to the present inventionadvantageously can be used in an audiovisual or multimedia entertainmentsystem. In particular, since each user advantageously can select his orher preferred view point and direction of view, multiple users canreceive a single set of full-surround image data and generatecorresponding multiple display images, in either linear or circularperspective.

Although presently preferred embodiments of the present invention havebeen described in detail hereinabove, it should be clearly understoodthat many variations and/or modifications of the basic inventiveconcepts herein taught, which may appear to those skilled in thepertinent art, will still fall within the spirit and scope of thepresent invention, as defined in the appended claims.

What is claimed is:
 1. A method of modeling of the visible world usingfull-surround image data, said method comprising: selecting a view pointwithin a p-surface; and texture mapping full-surround image data ontosaid p-surface such that the resultant texture map is substantiallyequivalent to projecting full-surround image data onto the p-surfacefrom said view point to thereby generate a texture mapped p-surface. 2.The method as recited in claim 1, further comprising rotating saidtexture mapped p-surface so as to simulate rotating the direction ofview in the opposite direction.
 3. The method as recited in claim 1,wherein said selecting step comprises selecting the view point and adirection of view, and wherein said method further comprisesinteractively changing said direction of view to thereby expose acorresponding portion of said texture mapped p-surface.
 4. The method asrecited in claim 1, further comprising displaying a predeterminedportion of said texture mapped p-surface.
 5. The method as recited inclaim 4, wherein a viewer is allowed to interactively alter at least oneof focal length or an angle of view relative to said textured mappedp-surface to thereby vary the displayed portion of said texture mappedp-surface.
 6. The method as recited in claim 1, further comprising:displaying a predetermined portion of said p-surface: selecting a newviewpoint; repeating said texture mapping step using said new viewpoint;and redisplaying said predetermined portion of said p-surface, whereby afirst image portion occupying said predetermined portion displayedduring the displaying step is different than a second image portionoccupying said predetermined portion during the redisplaying step. 7.The method as recited in claim 6, wherein said selecting step comprisesinteractively selecting said new viewpoint.
 8. The method as recited inclaim 7, wherein a first said texture mapped p-surface is replaced by asecond texture mapped p-surface by interactively selecting said newviewpoint from viewpoints within said second texture mapped p-surface.9. The method as recited in claim 1, further comprising: selecting a newviewpoint; and displaying said texture mapped p-surface from said newviewpoint.
 10. The method as recited in claim 9, wherein the newviewpoint is close to the surface of said p-surface.
 11. A method ofmodeling of the visible world using full-surround image data,comprising: providing said full surround image data; selecting a viewpoint within a p-surface; texture mapping full-surround image data ontosaid p-surface such that the resultant texture map is substantiallyequivalent to projecting full-surround image data onto the p-surfacefrom said view point to thereby generate a texture mapped p-sphere; anddisplaying a predetermined portion of said texture mapped p-sphere. 12.The method as recited in claim 11, further comprising rotating saidtexture mapped p-sphere so as to simulate rotating the direction of viewin the opposite direction.
 13. The method as recited in claim 11,wherein said selecting step comprises selecting the view point and adirection of view, and wherein said method further comprisesinteractively changing said direction of view to thereby display anotherportion of said texture mapped p-sphere.
 14. The method as recited inclaim 11, further comprising: selecting a new viewpoint; and repeatingsaid texture mapping and said displaying steps using said new viewpoint.15. The method as recited in claim 14, wherein a first said texturemapped p-sphere is replaced by a second said texture mapped p-sphere byinteractively selecting said new viewpoint from viewpoints within saidsecond texture mapped p-sphere.
 16. The method as recited in claim 11,further comprising: selecting a new viewpoint; and displaying saidpredetermined portion of said texture mapped p-surface using said newviewpoint.
 17. The method as recited in claim 16, wherein said selectingstep comprises interactively selecting said new viewpoint.
 18. Anapparatus for modeling the visible world using full-surround image data,comprising: means for selecting a view point within a p-surface; meansfor texture mapping full-surround image data onto said p-surface suchthat the resultant texture map is substantially equivalent to projectingfull-surround image data onto the p-surface from said view point tothereby generate a texture mapped p-sphere; and means for displaying apredetermined portion of said texture mapped p-sphere.
 19. The apparatusas recited in claim 18, wherein said selecting means comprises means forselecting said view point and interactively selecting a direction ofview to thereby interactively display portions of said texture mappedp-surface p-sphere.
 20. The apparatus as recited in claim 19, furthercomprising means for replacing a first said texture mapped p-sphere by asecond said texture mapped p-sphere by interactively selecting saidviewpoint from a plurality of viewpoints within said second texturemapped p-sphere.
 21. The apparatus as recited in claim 18, wherein saidselecting means permits interactive selection of said viewpoint.
 22. Theapparatus as recited in claim 18, wherein said selecting means comprisesmeans for selecting said view point and interactively selecting adirection of view to thereby interactively display said predeterminedportion of said texture mapped p-sphere.